Related papers: Lorentz-boost eigenmodes
A relativistic particle undergoing successive boosts which are non collinear will experience a rotation of its coordinate axes with respect to the boosted frame. This rotation of coordinate axes is caused by a relativistic phenomenon called…
As is well known, there exist some Lorentz breaking scenarios which explain the smallness of the cosmological constant in the present era. An important aspect to analyze is the propagation of gravitational waves and the screening or…
A static rotating cosmic string metric is singular along a timelike line and fails to be globally hyperbolic; these features make it difficult to solve the wave equation by conventional energy methods. Working on a single angular mode at a…
We study the structure of maps that Lorentz boosts induce on the spin degree of freedom of a system consisting of two massive spin-$1/2$ particles. We consider the case where the spin state is described by the Werner state and the momenta…
We examine a collection of particles interacting with inverse-square two-body potentials in the thermodynamic limit. We find explicit large-amplitude density waves and soliton solutions for the motion of the system. Waves can be constructed…
Boost-rotation symmetric spacetimes are exceptional as they are the only exact asymptotically flat solutions to the Einstein equations describing spatially bounded sources ("point-like" particles, black holes) undergoing non-trivial motion…
A 2D temporal incompressible stability analysis is carried out for lobed jets. The jet base flow is assumed to be parallel and of a vortex-sheet type. The eigenfunctions of this simplified stability problem are expanded using the…
We investigate the effects of the repeated application of Lorentz-boosts to the four momentum of a photon in the transverse direction and observe that this can take us to a reference frame in which the direction of the photon's momentum is…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
It is possible to associate two angles with two successive non-collinear Lorentz boosts. If one boost is applied after the initial boost, the result is the final boost preceded by a rotation called the Wigner rotation. The other rotation is…
Basic models which give rise to one- and two-dimensional (1D and 2D) solitons, such as the Gross-Pitaevskii (GP) equations for Bose-Einstein condensates (BECs), feature the Galilean invariance, which makes it possible to generate families…
We consider two types of the time-dependent Ginzburg-Landau equation in 2D bounded domains: the heat-flow equation and the Schroedinger equation. The system of ordinary differential equations is obtained that describes the evolution of the…
The Classical Coordinate System is geometrical by nature with time being an external variable. Constructing a classical coordinate system employs a point-like signal with infinite speed. In Special Relativity Theory the speed is limited but…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
Hydrodynamics of gases in the classical domain are examined from the perspective that the gas has a well-defined wavefunction description at all times. Specifically, the internal energy and volume exclusion of decorrelated vortex structures…
We study vortices in p-wave superconductors in a Ginzburg-Landau setting. The state of the superconductor is described by a pair of complex wave functions, and the p-wave symmetric energy functional couples these in both the kinetic…
The propagation of a spherical wave through a two-dimensional random Lorentz gas composed of small fixed scatterers is studied. Inspired by the Mott problem (how an initially isotropic quantum wave can give rise to a single particle-like…
We consider the ground-state properties of the two-component spin-orbit coupled ultracold bosons subject to a rotationally symmetric in-plane gradient magnetic field. In the non-interacting case, the ground state supports giant-vortices…
Boost-rotation symmetric spacetimes are the only locally asymptotically flat axially symmetric electrovacuum spacetimes with a further symmetry that are radiative. They are realized by uniformly accelerated particles of various kinds or…
In this thesis, we consider the dynamics of vortices in the easy plane insulating ferromagnet in two dimensions. In addition to the quasiparticle excitations, here spin waves or magnons, this magnetic system admits a family of vortex…